Elaborting on TheBridge's answer you should be aware that one of the 'easy' ways to check a process is a brownian motion is to use Levy's Characterization theorem: almostsure.wordpress.com/2010/04/13/…. Computationally the majority of the proof can be reduced to checking the quadratic variation $[X]_t =t$.
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user7980Sep 25 '11 at 1:56